This whole thread exists because the public bus system is a failure in the US. How many threads on car dependence has there been on HN? The bus system is used only by the lowest income members of society who can't afford a car. They suffer long transit times, lack of point-to-point mobility, and delays. Sure that "works" to some extent for those who have no other options. And this leads to other effects like decreased health and social mobility. Want to go to college after work to improve your life? Can't because the bus routes take 2x or 3x the time it would in a car to get there. Want to get a checkup for that cough? Again riding the bus takes too much time.
You can't force a top-down solution for public transit with the road system in the US. The great strength of the US road system is point-to-point transportation. Let everyone benefit from that instead of running buses that only the poorest use. Publicly funded rideshare is the way to do this. After a while, the bus routes will naturally appear in the data. This is the bottom-up way to build a bus system.
My main problem with ride sharing is that it allows companies to compete with taxi's by exploiting car owner needing extra income.
In the Netherlands we treat public transport as a basic necessity that should be available to everyone. Not everyone can own or drive a car (too old, too young, too poor, physically or mentally not able, hazard on the road for others), and you don’t want to force everyone to move to large cities where public transport is available: cities are more expensive. In addition, public transport usually has less impact on the environment.
Bussed are sized to need though: areas with lower demand are served by smaller, less frequent busses, or busses on demand. You need to call to reserve a ride. Which is almost like ride sharing, but not at the cost of ride sharing car owners.
Public transport has a large positive impact on a society, and as such doesn’t really need to make a profit. E.g., we all benefit if teachers that can’t afford to live in cites, can still travels into cities to teach children there. The entire society, including the economy, benefits from having the population educated well.
As far as I can tell many people are using public transport, including buses, so it seems to work to some extend.